A globe is definitely accurate.
The standard maps are inaccurate because the world is round, and maps are flat. There’s no way to project a spherical map on a flat surface without stretching or tearing parts of the map. In the former case you get maps like the [Mercator projection](https://en.wikipedia.org/wiki/Mercator_projection) which makes areas closer to the poles huge, and in the latter case you get odd things like [this](https://en.wikipedia.org/wiki/Goode_homolosine_projection).
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